Metrics for Falkner and Boettcher, Equation (22+)

analyze4.0ms (0%)

Memory

8.5MiB live, 8.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample1.1s (12.2%)

Memory

38.3MiB live, 1 671.8MiB allocated

Samples

706.0ms	8 256×	0	valid
1.0ms	14×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 543.0ms

ival-mult: 259.0ms (47.7% of total)

ival-sub: 75.0ms (13.8% of total)

ival-div: 69.0ms (12.7% of total)

ival-sqrt: 68.0ms (12.5% of total)

ival-pi: 49.0ms (9% of total)

exact: 15.0ms (2.8% of total)

ival-true: 6.0ms (1.1% of total)

ival-assert: 3.0ms (0.6% of total)

Bogosity

preprocess324.0ms (3.7%)

Memory

-30.4MiB live, 481.1MiB allocated

Algorithm

1×	egg-herbie

Rules

4 898×	`lower-fma.f64`
4 898×	`lower-fma.f32`
2 702×	`lower-*.f32`
2 692×	`lower-*.f64`
1 796×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	40
1	59	37
2	176	36
3	654	36
4	2038	36
5	4182	36
6	6384	36
7	7270	36
0	16	20
0	26	20
1	51	18
2	118	18
3	318	18
4	896	18
5	1509	18
6	2857	18
7	5680	18
8	7756	18
0	8271	16

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Calls

Call 1

Inputs

(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))

Outputs

(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))

(/.f64 #s(literal -4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)))))

Symmetry

(abs v)

explain217.0ms (2.5%)

Memory

-34.0MiB live, 254.2MiB allocated

FPErrors

Click to see full error table

Overpredictions	Example	Example	Subexpression
0	-	-	`#s(literal 3 binary64)`
0	-	-	`(*.f64 v v)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`#s(literal 4 binary64)`
0	-	-	`(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))`
0	-	-	`(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))`
0	-	-	`(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))`
0	-	-	`(*.f64 #s(literal 3 binary64) (PI.f64))`
0	-	-	`#s(literal 6 binary64)`
0	-	-	`v`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))`
2	(1.0327901458069277e-162)	-	`(.f64 #s(literal 6 binary64) (.f64 v v))`
0	-	-	`(-.f64 #s(literal 1 binary64) (*.f64 v v))`
0	-	-	`(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))`
0	-	-	`(PI.f64)`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

70.0ms

512×

valid

Compiler

Compiled 216 to 68 computations (68.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 30.0ms (57.7% of total)

ival-sqrt: 11.0ms (21.2% of total)

ival-sub: 5.0ms (9.6% of total)

ival-div: 3.0ms (5.8% of total)

ival-pi: 2.0ms (3.8% of total)

exact: 1.0ms (1.9% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Status

Accuracy

Program

▶

98.5%

(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))

Compiler

Compiled 21 to 16 computations (23.8% saved)

simplify362.0ms (4.2%)

Memory

34.1MiB live, 305.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
✓	cost-diff	128	(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
✓	cost-diff	128	(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓	cost-diff	320	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Rules

4 898×	`lower-fma.f64`
4 898×	`lower-fma.f32`
2 702×	`lower-*.f32`
2 692×	`lower-*.f64`
1 796×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	85
0	26	85
1	51	83
2	118	83
3	318	83
4	896	83
5	1509	83
6	2857	83
7	5680	83
8	7756	83
0	8271	76

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
#s(literal 4 binary64)
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 #s(literal 3 binary64) (PI.f64))
#s(literal 3 binary64)
(PI.f64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
#s(literal 2 binary64)
(.f64 #s(literal 6 binary64) (.f64 v v))
#s(literal 6 binary64)

Outputs
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
(/.f64 #s(literal -4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)))))
#s(literal 4 binary64)
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
(.f64 (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(*.f64 #s(literal 3 binary64) (PI.f64))
#s(literal 3 binary64)
(PI.f64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 #s(literal 6 binary64) (.f64 v v))
(.f64 (.f64 v v) #s(literal 6 binary64))
#s(literal 6 binary64)

localize73.0ms (0.8%)

Memory

6.1MiB live, 44.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
✓	accuracy	99.7%	(.f64 #s(literal 6 binary64) (.f64 v v))
✓	accuracy	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Samples

55.0ms

256×

valid

Compiler

Compiled 87 to 18 computations (79.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 7.0ms (49.5% of total)

ival-sub: 2.0ms (14.1% of total)

ival-div: 2.0ms (14.1% of total)

ival-sqrt: 2.0ms (14.1% of total)

ival-pi: 1.0ms (7.1% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory

7.3MiB live, 7.3MiB allocated

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))>
#<alt (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))>
#<alt (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))>
#<alt (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))>
#<alt (.f64 #s(literal 6 binary64) (.f64 v v))>
#<alt (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))>

Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))>
#<alt (* 3 (PI))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt 2>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* 3 (* (PI) (sqrt 2)))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))>
#<alt (* -3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* 3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	v	@	inf	(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
2.0ms	v	@	0	(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
1.0ms	v	@	0	(* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))
1.0ms	v	@	0	(* (* 3 (PI)) (- 1 (* v v)))
1.0ms	v	@	inf	(* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))

simplify730.0ms (8.4%)

Memory

-6.6MiB live, 722.9MiB allocated

Algorithm

1×	egg-herbie

Rules

15 354×	`lower-fma.f64`
15 354×	`lower-fma.f32`
6 176×	`lower-+.f64`
6 176×	`lower-+.f32`
5 400×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	241	1610
1	747	1426
2	2954	1351
0	8247	1301

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 3 (PI))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* 3 (* (PI) (sqrt 2)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))

Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(.f64 #s(literal 4/3 binary64) (fma.f64 (fma.f64 v (/.f64 (.f64 v #s(literal 27/16 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))) (.f64 v v) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(fma.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (.f64 (fma.f64 #s(literal 4/3 binary64) (fma.f64 (.f64 v v) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 27/8 binary64) (PI.f64)) (/.f64 #s(literal 135/16 binary64) (PI.f64)))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))) (/.f64 #s(literal 9/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (.f64 (.f64 v v) (.f64 v v))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (PI.f64) (.f64 v (.f64 v v))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (fma.f64 #s(literal 4/3 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 #s(literal 1/27 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (.f64 v v))) (.f64 v (.f64 v v)))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (.f64 (.f64 v v) (.f64 v v)))) (/.f64 (.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64))) (.f64 v (.f64 v v)))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(/.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (.f64 (.f64 v v) (.f64 v v)))) (/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (PI.f64)) (/.f64 #s(literal 5/1296 binary64) (PI.f64))) (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64)))) (/.f64 (.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64))) (.f64 v (*.f64 v v)))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (PI.f64) (.f64 v (.f64 v v))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (fma.f64 #s(literal 4/3 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 #s(literal 1/27 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (.f64 v v))) (neg.f64 (.f64 v (.f64 v v))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(/.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (.f64 (.f64 v v) (.f64 v v)))) (/.f64 (.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64))) (neg.f64 (.f64 v (.f64 v v))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(/.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (.f64 (.f64 v v) (.f64 v v)))) (/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (PI.f64)) (/.f64 #s(literal 5/1296 binary64) (PI.f64))) (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64)))) (/.f64 (.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64))) (neg.f64 (.f64 v (*.f64 v v))))
(* 3 (PI))
(*.f64 (PI.f64) #s(literal 3 binary64))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(* -3 (* (pow v 2) (PI)))
(.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal -3 binary64)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* -3 (* (pow v 2) (PI)))
(.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal -3 binary64)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
2
#s(literal 2 binary64)
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* -6 (pow v 2))
(.f64 (.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* -6 (pow v 2))
(.f64 (.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* 3 (* (PI) (sqrt 2)))
(.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(.f64 #s(literal 3 binary64) (fma.f64 (.f64 v v) (.f64 (PI.f64) (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(.f64 #s(literal 3 binary64) (fma.f64 (fma.f64 (.f64 v v) (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/4 binary64)) (.f64 (PI.f64) (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 v v) (.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(fma.f64 (.f64 v v) (.f64 #s(literal 3 binary64) (fma.f64 (fma.f64 (.f64 v v) (fma.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 9/4 binary64) (/.f64 (.f64 (PI.f64) #s(literal -27/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64)))) (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/4 binary64))) (.f64 v v) (.f64 (PI.f64) (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))) (.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(.f64 (.f64 v (.f64 v v)) (.f64 (PI.f64) (*.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal 3 binary64) (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (.f64 (PI.f64) (*.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(.f64 v (.f64 (.f64 v v) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (*.f64 v v))))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))) (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v)))) (/.f64 (.f64 #s(literal -3/2 binary64) (+.f64 (/.f64 (PI.f64) (.f64 #s(literal -6 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (pow.f64 v #s(literal 6 binary64))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(.f64 (.f64 v (.f64 v v)) (.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal 3 binary64)))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(.f64 (fma.f64 #s(literal 3 binary64) (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))))) (neg.f64 (.f64 v (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(.f64 (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v)))))) (neg.f64 (.f64 v (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(.f64 (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))) (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v)))) (/.f64 (.f64 #s(literal -3/2 binary64) (+.f64 (/.f64 (PI.f64) (.f64 #s(literal -6 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (pow.f64 v #s(literal 6 binary64))))) (neg.f64 (.f64 v (.f64 v v))))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(.f64 v (.f64 v #s(literal 6 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 (*.f64 v v) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (fma.f64 #s(literal -27/2 binary64) (/.f64 (*.f64 v v) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(+.f64 (/.f64 v (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))) (.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))) (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))))
(* -1 (* v (sqrt -6)))
(neg.f64 (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(neg.f64 (fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))) (neg.f64 v))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(.f64 v (neg.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))) (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))))

rewrite927.0ms (10.7%)

Memory

-204.5MiB live, 567.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 770×	`lower-*.f32`
4 760×	`lower-*.f64`
4 634×	`lower-fma.f64`
4 634×	`lower-fma.f32`
2 134×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	67
0	26	67
1	101	65
2	626	65
3	5771	65
0	8439	58

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

6 → 487

Calls

Call 1

Inputs
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
(.f64 #s(literal 6 binary64) (.f64 v v))
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))) #s(literal 3/4 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))))
(neg.f64 (/.f64 #s(literal -4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal -4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))))
(neg.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
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(.f64 (.f64 #s(literal 3 binary64) (fma.f64 v v #s(literal 1 binary64))) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (.f64 (cbrt.f64 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64)))))
(.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64)))))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (fma.f64 v v #s(literal 1 binary64))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (PI.f64))
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))) #s(literal 3 binary64))
(.f64 (neg.f64 (.f64 (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))) #s(literal -3 binary64))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))) (.f64 #s(literal 3 binary64) (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(.f64 (neg.f64 (.f64 (PI.f64) #s(literal -3 binary64))) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))) (pow.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)) (.f64 #s(literal 3 binary64) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (.f64 #s(literal 3 binary64) (fma.f64 v v #s(literal 1 binary64)))) (PI.f64))
(.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 #s(literal 3 binary64) (PI.f64)))
(.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 3 binary64) (cbrt.f64 (PI.f64))))
(.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))) (sqrt.f64 (PI.f64))) (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))))
(.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))) (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal 1 binary64))) (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal 1 binary64)) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (fma.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v))))) (/.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 1 binary64))))
(.f64 #s(literal 1 binary64) (.f64 v (*.f64 v #s(literal 6 binary64))))
(.f64 v (.f64 v #s(literal 6 binary64)))
(.f64 (.f64 v v) #s(literal 6 binary64))
(.f64 #s(literal 6 binary64) (.f64 v v))
(.f64 (.f64 v (*.f64 v #s(literal 6 binary64))) #s(literal 1 binary64))
(.f64 (.f64 v #s(literal 6 binary64)) v)
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 (log.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64))) (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (*.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64))) (sqrt.f64 (fma.f64 (.f64 v v) (fma.f64 (*.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64))) (sqrt.f64 (fma.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) (-.f64 (.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -8 binary64) (.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -4 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 36 binary64))))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (.f64 v v) (fma.f64 (*.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64))) (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (*.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64)))) #s(literal -1 binary64))
(.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64))) (pow.f64 (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 216 binary64) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64))) (pow.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))

eval76.0ms (0.9%)

Memory: 23.8MiB live, 213.6MiB allocated
Compiler: Compiled 16 895 to 1 903 computations (88.7% saved)

prune96.0ms (1.1%)

Memory

-6.8MiB live, 201.5MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	554	5	559
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	555	5	560

Accuracy

100.0%

Counts

560 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
▶	97.6%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
▶	99.1%	(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
▶	100.0%	(.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))) (fma.f64 v v #s(literal 1 binary64)))
▶	97.6%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Compiler

Compiled 176 to 132 computations (25% saved)

simplify326.0ms (3.8%)

Memory

-5.4MiB live, 596.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 3 binary64) (PI.f64))
✓	cost-diff	0	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
✓	cost-diff	128	(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓	cost-diff	192	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓	cost-diff	0	(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
✓	cost-diff	0	#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))
✓	cost-diff	0	(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v)))))
✓	cost-diff	0	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
✓	cost-diff	128	(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
✓	cost-diff	0	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓	cost-diff	0	(.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))) (fma.f64 v v #s(literal 1 binary64)))
✓	cost-diff	384	(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v))))))

Rules

4 208×	`lower-*.f32`
4 178×	`lower-*.f64`
4 006×	`lower-fma.f32`
4 000×	`lower-fma.f64`
2 506×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	388
0	89	371
1	170	357
2	360	357
3	889	357
4	2589	357
5	3772	357
6	7279	357
0	8390	350

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))) (fma.f64 v v #s(literal 1 binary64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v))))))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
#s(literal 4/3 binary64)
(PI.f64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v)))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v))))
#s(literal 1 binary64)
(.f64 v (.f64 v (*.f64 v v)))
(.f64 v (.f64 v v))
(*.f64 v v)
(fma.f64 v v #s(literal 1 binary64))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 4/3 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(PI.f64)
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
#s(literal 4 binary64)
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v)))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))
(*.f64 (PI.f64) #s(literal 3 binary64))
(PI.f64)
#s(literal 3 binary64)
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
#s(literal 2 binary64)
(.f64 #s(literal 6 binary64) (.f64 v v))
#s(literal 6 binary64)
(*.f64 v v)
v
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
#s(literal 4/3 binary64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))
(PI.f64)
(fma.f64 v v #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
#s(literal 4 binary64)
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 #s(literal 3 binary64) (PI.f64))
#s(literal 3 binary64)
(PI.f64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
(fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)

Outputs
(.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))) (fma.f64 v v #s(literal 1 binary64)))
(/.f64 (fma.f64 #s(literal 4/3 binary64) (.f64 v v) #s(literal 4/3 binary64)) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v)))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v))))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
#s(literal 4/3 binary64)
(PI.f64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v)))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v)))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v))))
#s(literal 1 binary64)
(.f64 v (.f64 v (*.f64 v v)))
(.f64 v (.f64 v v))
(*.f64 v v)
(fma.f64 v v #s(literal 1 binary64))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 4/3 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(PI.f64)
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
#s(literal 4 binary64)
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v)))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))
(*.f64 (PI.f64) #s(literal 3 binary64))
(PI.f64)
#s(literal 3 binary64)
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 #s(literal 6 binary64) (.f64 v v))
(.f64 (.f64 v v) #s(literal 6 binary64))
#s(literal 6 binary64)
(*.f64 v v)
v
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (fma.f64 (PI.f64) (*.f64 v v) (PI.f64))))
#s(literal 4/3 binary64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (fma.f64 (PI.f64) (*.f64 v v) (PI.f64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))
(fma.f64 (PI.f64) (*.f64 v v) (PI.f64))
(PI.f64)
(fma.f64 v v #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (neg.f64 (.f64 (.f64 (fma.f64 v v #s(literal -1 binary64)) (PI.f64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))))
#s(literal 4 binary64)
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(*.f64 #s(literal 3 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 3 binary64))
#s(literal 3 binary64)
(PI.f64)
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)

localize163.0ms (1.9%)

Memory

-3.9MiB live, 352.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
✓	accuracy	100.0%	(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
✓	accuracy	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓	accuracy	100.0%	(*.f64 v #s(literal -6 binary64))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	100.0%	(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
✓	accuracy	99.7%	(.f64 #s(literal 6 binary64) (.f64 v v))
✓	accuracy	99.1%	#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))
✓	accuracy	98.5%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.1%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
✓	accuracy	98.4%	(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
✓	accuracy	100.0%	(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v))))))
✓	accuracy	99.9%	(.f64 v (.f64 v (*.f64 v v)))
✓	accuracy	99.9%	(.f64 v (.f64 v v))
✓	accuracy	98.4%	(/.f64 #s(literal 4/3 binary64) (PI.f64))

Samples

82.0ms

256×

valid

Compiler

Compiled 390 to 45 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-mult: 26.0ms (46.2% of total)

ival-div: 10.0ms (17.8% of total)

ival-sqrt: 8.0ms (14.2% of total)

const: 4.0ms (7.1% of total)

ival-add: 3.0ms (5.3% of total)

ival-sub: 3.0ms (5.3% of total)

ival-pi: 1.0ms (1.8% of total)

exact: 1.0ms (1.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series16.0ms (0.2%)

Memory

25.9MiB live, 25.9MiB allocated

Counts

26 → 240

Calls

Call 1

Inputs
#<alt (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v))))))>
#<alt (.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))) (fma.f64 v v #s(literal 1 binary64)))>
#<alt (/.f64 #s(literal 4/3 binary64) (PI.f64))>
#<alt (PI.f64)>
#<alt #s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))>
#<alt (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))>
#<alt (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 #s(literal 1/2 binary64))>
#<alt (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))>
#<alt (/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))>
#<alt (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v)))))>
#<alt #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))>
#<alt (/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))>
#<alt (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))>
#<alt (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))>
#<alt (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))>
#<alt (/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))>
#<alt (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))>
#<alt (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))>
#<alt (*.f64 #s(literal 3 binary64) (PI.f64))>
#<alt (.f64 v (.f64 v v))>
#<alt (.f64 v (.f64 v (*.f64 v v)))>
#<alt (.f64 #s(literal 6 binary64) (.f64 v v))>
#<alt (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))>
#<alt (*.f64 v #s(literal -6 binary64))>
#<alt (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))>

Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 5) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (+ (* 4/3 (/ (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))))) (pow v 5))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 5) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (+ (* 4/3 (/ (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))))) (pow v 5)))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
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#<alt (* -1 (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt 2>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))>
#<alt (* 3 (PI))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* 3 (* (PI) (sqrt 2)))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))>
#<alt (* -3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* 3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))>
#<alt (pow v 3)>
#<alt (pow v 3)>
#<alt (pow v 3)>
#<alt (pow v 3)>
#<alt (pow v 3)>
#<alt (pow v 3)>
#<alt (pow v 3)>
#<alt (pow v 3)>
#<alt (pow v 3)>
#<alt (pow v 3)>
#<alt (pow v 3)>
#<alt (pow v 3)>
#<alt (pow v 4)>
#<alt (pow v 4)>
#<alt (pow v 4)>
#<alt (pow v 4)>
#<alt (pow v 4)>
#<alt (pow v 4)>
#<alt (pow v 4)>
#<alt (pow v 4)>
#<alt (pow v 4)>
#<alt (pow v 4)>
#<alt (pow v 4)>
#<alt (pow v 4)>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>

Calls

60 calls:

Time	Variable		Point	Expression
2.0ms	v	@	inf	(/ (/ 4/3 (PI)) (* (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v))))))
1.0ms	v	@	inf	(/ 4/3 (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))))
1.0ms	v	@	0	(/ 4/3 (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))))
1.0ms	v	@	0	(/ (/ 4/3 (PI)) (* (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v))))))
0.0ms	v	@	inf	(* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1)))

simplify713.0ms (8.2%)

Memory

-9.7MiB live, 947.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 068×	`lower-fma.f64`
10 068×	`lower-fma.f32`
6 414×	`lower-*.f64`
6 414×	`lower-*.f32`
3 420×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	382	6348
1	1234	5398
2	5051	5163
0	8358	4975

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 5) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (+ (* 4/3 (/ (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))))) (pow v 5))
(* 4/3 (/ (sqrt -1/6) (* (pow v 5) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (+ (* 4/3 (/ (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))))) (pow v 5)))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
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(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
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(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 3 (* (PI) (sqrt 2)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(* 3 (PI))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))
(/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3)))
(* -1 (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3)))
(* (PI) (sqrt 2))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(* (pow v 3) (* (PI) (sqrt -6)))
(* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))))
(* -1 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 3 (PI))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* 3 (* (PI) (sqrt 2)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(pow v 3)
(pow v 3)
(pow v 3)
(pow v 3)
(pow v 3)
(pow v 3)
(pow v 3)
(pow v 3)
(pow v 3)
(pow v 3)
(pow v 3)
(pow v 3)
(pow v 4)
(pow v 4)
(pow v 4)
(pow v 4)
(pow v 4)
(pow v 4)
(pow v 4)
(pow v 4)
(pow v 4)
(pow v 4)
(pow v 4)
(pow v 4)
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))

Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(fma.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (/ 1 (* (PI) (sqrt 1/2))))))
(fma.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (.f64 (.f64 v v) (fma.f64 (.f64 v v) (fma.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 9/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(fma.f64 v (fma.f64 v (.f64 #s(literal 4/3 binary64) (.f64 (+.f64 (fma.f64 (.f64 v v) (+.f64 (/.f64 #s(literal 135/32 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 #s(literal 3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 #s(literal 27/16 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (.f64 v v))) (/.f64 v (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(* -4/3 (/ (sqrt -1/6) (* (pow v 5) (PI))))
(/.f64 (.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (PI.f64) (pow.f64 v #s(literal 5 binary64))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5))
(/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (.f64 v (.f64 v (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))))) (pow.f64 v #s(literal 5 binary64)))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5))
(/.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 (.f64 v v) (.f64 v v))) (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (.f64 v (.f64 v (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))))))) (pow.f64 v #s(literal 5 binary64)))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (+ (* 4/3 (/ (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))))) (pow v 5))
(/.f64 (+.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 (.f64 v v) (.f64 v v))) (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (.f64 v (.f64 v (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))))))) (/.f64 (+.f64 (/.f64 #s(literal 5/1944 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (pow.f64 v #s(literal 6 binary64)))) (pow.f64 v #s(literal 5 binary64)))
(* 4/3 (/ (sqrt -1/6) (* (pow v 5) (PI))))
(/.f64 (.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (PI.f64) (pow.f64 v #s(literal 5 binary64))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5)))
(/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (.f64 v (.f64 v (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))))) (neg.f64 (pow.f64 v #s(literal 5 binary64))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5)))
(/.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 (.f64 v v) (.f64 v v))) (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (.f64 v (.f64 v (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))))))) (neg.f64 (pow.f64 v #s(literal 5 binary64))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (+ (* 4/3 (/ (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))))) (pow v 5)))
(/.f64 (+.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/144 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (.f64 (.f64 v v) (.f64 v v))) (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (.f64 v (.f64 v (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))))))) (/.f64 (+.f64 (/.f64 #s(literal 5/1944 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (pow.f64 v #s(literal 6 binary64)))) (neg.f64 (pow.f64 v #s(literal 5 binary64))))
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(.f64 #s(literal 4/3 binary64) (fma.f64 v (/.f64 (.f64 v #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(.f64 #s(literal 4/3 binary64) (fma.f64 (fma.f64 v (/.f64 (.f64 v #s(literal 27/16 binary64)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))) (.f64 v v) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
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(neg.f64 (.f64 (.f64 v (.f64 v v)) (fma.f64 (PI.f64) (.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (.f64 #s(literal 3 binary64) (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))) (*.f64 v v)))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(.f64 (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v)))) (.f64 #s(literal -3 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))) (neg.f64 (.f64 v (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(.f64 (fma.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 v v)) (+.f64 (/.f64 (.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (.f64 (.f64 v v) (.f64 v v))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))) (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal 1/12 binary64))) (pow.f64 v #s(literal 6 binary64))))) (.f64 #s(literal -3 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))) (neg.f64 (.f64 v (.f64 v v))))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 3)
(.f64 v (.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(pow v 4)
(.f64 (.f64 v v) (*.f64 v v))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(.f64 (.f64 v v) #s(literal 6 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 (*.f64 v v) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (fma.f64 #s(literal -27/2 binary64) (/.f64 (*.f64 v v) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))))
(* -1 (* v (sqrt -6)))
(*.f64 (sqrt.f64 #s(literal -6 binary64)) (neg.f64 v))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(neg.f64 (fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))) (neg.f64 v))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))) (neg.f64 v))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 (*.f64 v v) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (fma.f64 #s(literal -27/2 binary64) (/.f64 (*.f64 v v) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))))
(* -1 (* v (sqrt -6)))
(*.f64 (sqrt.f64 #s(literal -6 binary64)) (neg.f64 v))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(neg.f64 (fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))) (neg.f64 v))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))) (neg.f64 v))

rewrite535.0ms (6.2%)

Memory

-20.1MiB live, 1 220.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 706×	`lower-*.f32`
4 682×	`lower-/.f32`
4 676×	`lower-*.f64`
4 670×	`lower-/.f64`
3 820×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	282
0	89	269
1	303	259
2	1837	256
0	8142	256

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

26 → 1 397

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v))))))
(.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))) (fma.f64 v v #s(literal 1 binary64)))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
(PI.f64)
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
(-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v)))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
(*.f64 #s(literal 3 binary64) (PI.f64))
(.f64 v (.f64 v v))
(.f64 v (.f64 v (*.f64 v v)))
(.f64 #s(literal 6 binary64) (.f64 v v))
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))
(*.f64 v #s(literal -6 binary64))
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v))))) (.f64 (PI.f64) #s(literal 3/4 binary64)))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v))))))) (.f64 #s(literal -1 binary64) (/.f64 #s(literal 4/3 binary64) (.f64 (PI.f64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))))))
(neg.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal 4/3 binary64) (.f64 (PI.f64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v)))))))))
(/.f64 #s(literal 4/3 binary64) (.f64 (PI.f64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))))
(/.f64 #s(literal 4/3 binary64) (neg.f64 (.f64 (neg.f64 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v))))))))
(/.f64 #s(literal 4/3 binary64) (neg.f64 (neg.f64 (.f64 (PI.f64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))))))
(/.f64 #s(literal 4/3 binary64) (neg.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v))))) (neg.f64 (PI.f64)))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (neg.f64 (neg.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v))))))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v))))) (*.f64 (PI.f64) #s(literal 3/4 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 (PI.f64) #s(literal 3/4 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (*.f64 v v)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (PI.f64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))) #s(literal 4/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v))))) (*.f64 (PI.f64) #s(literal 3/4 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))) (/.f64 #s(literal 4/3 binary64) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))))
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(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))) (sqrt.f64 (neg.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v #s(literal 6 binary64))) (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v #s(literal 6 binary64))) (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (*.f64 v v) #s(literal -12 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v (.f64 v #s(literal 6 binary64))) (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (*.f64 v v) #s(literal -12 binary64))))))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v (.f64 v #s(literal 6 binary64))) (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 v #s(literal -6 binary64))
(*.f64 #s(literal -6 binary64) v)
(exp.f64 (.f64 (log.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64))) (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 (.f64 v (.f64 v #s(literal 6 binary64))) (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64)) (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)) (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (*.f64 v v))) #s(literal 36 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (fma.f64 (.f64 v (.f64 v #s(literal 6 binary64))) (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (-.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)) (.f64 (*.f64 v v) #s(literal -12 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))) (sqrt.f64 (neg.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v #s(literal 6 binary64))) (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v #s(literal 6 binary64))) (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (*.f64 v v) #s(literal -12 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v (.f64 v #s(literal 6 binary64))) (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (*.f64 v v) #s(literal -12 binary64))))))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v (.f64 v #s(literal 6 binary64))) (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))

eval273.0ms (3.1%)

Memory: 34.0MiB live, 818.5MiB allocated
Compiler: Compiled 82 596 to 5 217 computations (93.7% saved)

prune260.0ms (3%)

Memory

-8.6MiB live, 595.6MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1 910	5	1 915
Fresh	0	0	0
Picked	4	1	5
Done	0	0	0
Total	1 914	6	1 920

Accuracy

100.0%

Counts

1 920 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
▶	97.6%	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
▶	98.5%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
▶	99.1%	(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
▶	97.6%	(.f64 #s(approx (/ (/ 4/3 (PI)) ( (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (fma.f64 v v #s(literal 1 binary64)))
✓	97.6%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Compiler

Compiled 160 to 125 computations (21.9% saved)

simplify274.0ms (3.2%)

Memory

8.8MiB live, 534.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 v v)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓	cost-diff	128	(.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
✓	cost-diff	320	(/.f64 #s(literal 4 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
✓	cost-diff	0	(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
✓	cost-diff	0	#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))))
✓	cost-diff	0	(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓	cost-diff	0	(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
✓	cost-diff	0	(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
✓	cost-diff	0	#s(approx (/ (/ 4/3 (PI)) (* (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
✓	cost-diff	0	(.f64 #s(approx (/ (/ 4/3 (PI)) ( (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (fma.f64 v v #s(literal 1 binary64)))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))

Rules

5 196×	`lower-fma.f32`
5 188×	`lower-fma.f64`
4 346×	`lower-*.f32`
4 324×	`lower-*.f64`
1 762×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	403
0	90	400
1	168	396
2	319	394
3	739	386
4	1627	386
5	2297	386
6	3948	386
7	5910	386
0	8098	385

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
#s(literal 4/3 binary64)
#s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
(PI.f64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 #s(approx (/ (/ 4/3 (PI)) ( (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (fma.f64 v v #s(literal 1 binary64)))
#s(approx (/ (/ 4/3 (PI)) (* (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 4/3 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(PI.f64)
(fma.f64 v v #s(literal 1 binary64))
v
#s(literal 1 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
#s(literal 4 binary64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))
(*.f64 (PI.f64) #s(literal 3 binary64))
(PI.f64)
#s(literal 3 binary64)
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
#s(literal 4 binary64)
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(PI.f64)
(fma.f64 (*.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))
(*.f64 v v)
v
#s(literal -3 binary64)
#s(literal 3 binary64)
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
(fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
#s(literal 4 binary64)
(.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
(.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(*.f64 (PI.f64) #s(literal 3 binary64))
(PI.f64)
#s(literal 3 binary64)
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)

Outputs
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
#s(literal 4/3 binary64)
#s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
(PI.f64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 #s(approx (/ (/ 4/3 (PI)) ( (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (fma.f64 v v #s(literal 1 binary64)))
#s(approx (/ (/ 4/3 (PI)) (* (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 4/3 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(PI.f64)
(fma.f64 v v #s(literal 1 binary64))
v
#s(literal 1 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
#s(literal 4 binary64)
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
v
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))
(*.f64 (PI.f64) #s(literal 3 binary64))
(PI.f64)
#s(literal 3 binary64)
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal -3 binary64) (.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)))))))
#s(literal 4 binary64)
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal -3 binary64) (.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64))))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 #s(literal -3 binary64) (.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)))))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(.f64 #s(literal -3 binary64) (.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64))))
(PI.f64)
(fma.f64 (*.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))
(*.f64 v v)
v
#s(literal -3 binary64)
#s(literal 3 binary64)
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)
(/.f64 #s(literal 4 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal -4/3 binary64) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)))))
#s(literal 4 binary64)
(.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (.f64 #s(literal -3 binary64) (.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)))))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
#s(literal 1 binary64)
(*.f64 v v)
v
(.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (*.f64 (PI.f64) #s(literal 3 binary64)))
(*.f64 (PI.f64) #s(literal 3 binary64))
(PI.f64)
#s(literal 3 binary64)
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
(*.f64 v #s(literal -6 binary64))
#s(literal -6 binary64)
#s(literal 2 binary64)

localize191.0ms (2.2%)

Memory

17.4MiB live, 328.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
✓	accuracy	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
✓	accuracy	100.0%	(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
✓	accuracy	98.5%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓	accuracy	100.0%	(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓	accuracy	99.1%	#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))
✓	accuracy	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	100.0%	(.f64 #s(approx (/ (/ 4/3 (PI)) ( (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (fma.f64 v v #s(literal 1 binary64)))
✓	accuracy	99.1%	#s(approx (/ (/ 4/3 (PI)) (* (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
✓	accuracy	98.4%	(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	100.0%	(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.2%	#s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))

Samples

120.0ms

256×

valid

Compiler

Compiled 365 to 50 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-mult: 27.0ms (34.9% of total)

ival-sub: 22.0ms (28.4% of total)

ival-div: 9.0ms (11.6% of total)

ival-sqrt: 8.0ms (10.3% of total)

ival-add: 5.0ms (6.5% of total)

const: 4.0ms (5.2% of total)

ival-pi: 1.0ms (1.3% of total)

exact: 1.0ms (1.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory

-19.0MiB live, 21.5MiB allocated

Counts

24 → 228

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (PI.f64)>
#<alt (.f64 #s(approx (/ (/ 4/3 (PI)) ( (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (fma.f64 v v #s(literal 1 binary64)))>
#<alt #s(approx (/ (/ 4/3 (PI)) (* (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))>
#<alt (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))>
#<alt (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))>
#<alt (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))))>
#<alt (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))>
#<alt (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))>
#<alt (/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))>
#<alt (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))>
#<alt #s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))))>
#<alt (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))>
#<alt (/.f64 #s(literal 4 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))>
#<alt (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))>
#<alt (-.f64 #s(literal 1 binary64) (*.f64 v v))>
#<alt (*.f64 v v)>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))>
#<alt (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))>
#<alt (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))>

Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))>
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#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))>
#<alt (* 3 (* (PI) (sqrt 2)))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))>
#<alt (* -3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* 3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))>
#<alt (* 3 (PI))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* 3 (PI))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))>
#<alt (* 3 (* (PI) (sqrt 2)))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))>
#<alt (* -3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* 3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))>
#<alt 1>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (* -1 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* -1 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (* 3 (PI))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (* 3 (* (PI) (sqrt 2)))>
#<alt (+ (* -9 (/ (* (pow v 2) (PI)) (sqrt 2))) (* 3 (* (PI) (sqrt 2))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -9 (/ (PI) (sqrt 2))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -81/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -27/2 (/ (PI) (pow (sqrt 2) 3))))))))>
#<alt (* 3 (* v (* (PI) (sqrt -6))))>
#<alt (* v (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))>
#<alt (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))>
#<alt (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))))>
#<alt (* -3 (* v (* (PI) (sqrt -6))))>
#<alt (* -1 (* v (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))>
#<alt (* -1 (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))))>
#<alt (* -1 (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))))>

Calls

57 calls:

Time	Variable		Point	Expression
0.0ms	v	@	inf	(* (* (PI) 3) (sqrt (+ (* v (* v -6)) 2)))
0.0ms	v	@	0	(* (* (PI) 3) (sqrt (+ (* v (* v -6)) 2)))
0.0ms	v	@	inf	(* (PI) (+ (* (* v v) -3) 3))
0.0ms	v	@	0	(* (PI) (+ (* (* v v) -3) 3))
0.0ms	v	@	-inf	(* (* (PI) 3) (sqrt (+ (* v (* v -6)) 2)))

simplify543.0ms (6.3%)

Memory

26.3MiB live, 1 014.8MiB allocated

Algorithm

1×	egg-herbie

Rules

11 868×	`lower-fma.f64`
11 868×	`lower-fma.f32`
6 360×	`lower-*.f64`
6 360×	`lower-*.f32`
3 596×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	422	6836
1	1377	5844
2	5662	5636
0	8068	5423

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))
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(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
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(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
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(* (PI) (sqrt 2))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))
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(* (pow v 3) (* (PI) (sqrt -6)))
(* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))
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(* -1 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))
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(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
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(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
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(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 5) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (+ (* 4/3 (/ (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))))) (pow v 5))
(* 4/3 (/ (sqrt -1/6) (* (pow v 5) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6)))))) (pow v 5)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))) (pow v 4))) (+ (* 4/3 (/ (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))))) (pow v 5)))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 3 (* (PI) (sqrt 2)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
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(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
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(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
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(* 3 (* (PI) (sqrt 2)))
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(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
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(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
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(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
1
(+ 1 (* -1 (pow v 2)))
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(sqrt 2)
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(* v (sqrt -6))
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(* -1 (* v (sqrt -6)))
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(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -81/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -27/2 (/ (PI) (pow (sqrt 2) 3))))))))
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(* -3 (* v (* (PI) (sqrt -6))))
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Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
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(+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
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(.f64 #s(literal 4/3 binary64) (fma.f64 (fma.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (+.f64 (/.f64 #s(literal 27/16 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 #s(literal -3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))) (-.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (.f64 v v) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
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(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(* -3 (* (pow v 2) (PI)))
(.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal -3 binary64)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* -3 (* (pow v 2) (PI)))
(.f64 (PI.f64) (.f64 (*.f64 v v) #s(literal -3 binary64)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (.f64 v v)))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 #s(literal -3 binary64) (/.f64 (*.f64 v v) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (/.f64 (.f64 v v) (sqrt.f64 #s(literal 2 binary64))) #s(literal -9/4 binary64) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (fma.f64 #s(literal -27/2 binary64) (/.f64 (*.f64 v v) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(.f64 v (-.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 #s(literal -6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 v (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))))
(* -1 (* v (sqrt -6)))
(neg.f64 (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(neg.f64 (fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 (-.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 #s(literal -6 binary64) (sqrt.f64 #s(literal -6 binary64)))))) (neg.f64 v))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(neg.f64 (.f64 v (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))))
(* 3 (* (PI) (sqrt 2)))
(.f64 (PI.f64) (.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* -9 (/ (* (pow v 2) (PI)) (sqrt 2))) (* 3 (* (PI) (sqrt 2))))
(fma.f64 (PI.f64) (.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (.f64 (PI.f64) (.f64 v v)) #s(literal -9 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -9 (/ (PI) (sqrt 2))))))
(fma.f64 (.f64 v v) (fma.f64 v (.f64 v (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -27/4 binary64))) (/.f64 (.f64 (PI.f64) #s(literal -9 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (PI.f64) (.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -81/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -27/2 (/ (PI) (pow (sqrt 2) 3))))))))
(fma.f64 (PI.f64) (.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 v v) (fma.f64 v (.f64 v (fma.f64 (.f64 v v) (.f64 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) #s(literal -81/2 binary64)) (.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -27/4 binary64)))) (/.f64 (.f64 (PI.f64) #s(literal -9 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(* 3 (* v (* (PI) (sqrt -6))))
(.f64 v (.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))))
(* v (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))
(.f64 (.f64 v #s(literal 3 binary64)) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))
(* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))
(.f64 v (fma.f64 #s(literal 3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) #s(literal 1/4 binary64))))
(* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))))
(.f64 v (fma.f64 (PI.f64) (fma.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 3 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (fma.f64 (/.f64 (PI.f64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) #s(literal 1/4 binary64) (/.f64 (.f64 (PI.f64) #s(literal 3/2 binary64)) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))))))
(* -3 (* v (* (PI) (sqrt -6))))
(.f64 v (.f64 #s(literal -3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* v (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))
(.f64 v (.f64 #s(literal -3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))))
(* -1 (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))))
(neg.f64 (.f64 v (fma.f64 #s(literal 3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 (PI.f64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (.f64 (/.f64 (PI.f64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) #s(literal 1/4 binary64)))))
(* -1 (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))))
(.f64 (fma.f64 (PI.f64) (fma.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 3 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (fma.f64 (/.f64 (PI.f64) (.f64 (.f64 (.f64 v v) (.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) #s(literal 1/4 binary64) (/.f64 (.f64 (PI.f64) #s(literal 3/2 binary64)) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))))) (neg.f64 v))

rewrite576.0ms (6.6%)

Memory

12.3MiB live, 952.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 322×	`lower-*.f32`
5 300×	`lower-*.f64`
5 048×	`lower-/.f32`
5 038×	`lower-/.f64`
3 052×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	330
0	90	326
1	305	322
2	1775	322
0	8456	322

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

24 → 614

Calls

Call 1

Inputs
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
(PI.f64)
(.f64 #s(approx (/ (/ 4/3 (PI)) ( (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (fma.f64 v v #s(literal 1 binary64)))
#s(approx (/ (/ 4/3 (PI)) (* (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64))))
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64))))
(.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))
(/.f64 #s(literal 4 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(*.f64 v v)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
(.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))

Outputs
(exp.f64 (.f64 (log.f64 (.f64 #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3/4 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (neg.f64 (neg.f64 #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx ( (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3/4 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 #s(approx ( (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3/4 binary64)))))
(/.f64 #s(literal -4/3 binary64) (neg.f64 #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal -4/3 binary64) (neg.f64 (neg.f64 (neg.f64 #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 #s(approx ( (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3/4 binary64))))
(pow.f64 (.f64 #s(approx ( (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3/4 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) #s(approx ( (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) #s(approx ( (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 #s(literal -4/3 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx ( (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx ( (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))) #s(literal 4/3 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3/4 binary64)))))
#s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (log.f64 (PI.f64))))
(sqrt.f64 (.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 2 binary64)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (PI.f64))))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (PI.f64)))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (.f64 (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 (PI.f64) #s(literal 1 binary64))
(/.f64 (neg.f64 (PI.f64)) #s(literal -1 binary64))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
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(/.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64))) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -216 binary64)) #s(literal 8 binary64)))) (sqrt.f64 (neg.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -216 binary64)) #s(literal 8 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(pow.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)) (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -216 binary64)) #s(literal 8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (*.f64 v v) #s(literal -12 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (*.f64 v v) #s(literal -12 binary64))))))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -216 binary64)) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (*.f64 v v) #s(literal -12 binary64))))))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(.f64 (pow.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (.f64 (PI.f64) #s(literal 3 binary64))))
(.f64 (PI.f64) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))) #s(literal 3 binary64)))
(.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) (*.f64 (PI.f64) #s(literal 3 binary64)))
(.f64 #s(literal 3 binary64) (.f64 (PI.f64) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))))
(.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #s(literal 3 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (.f64 v v) #s(literal 2 binary64))) #s(literal 3 binary64))))
(.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64)))) #s(literal 3 binary64))
(.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))) #s(literal 3 binary64)) (PI.f64))

eval169.0ms (1.9%)

Memory: -14.1MiB live, 394.1MiB allocated
Compiler: Compiled 32 408 to 3 324 computations (89.7% saved)

prune200.0ms (2.3%)

Memory

-35.9MiB live, 342.2MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	1 139	0	1 139
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	1 139	6	1 145

Accuracy

100.0%

Counts

1 145 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.5%	(/.f64 #s(literal 4 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
✓	97.6%	(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
✓	98.5%	(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓	99.1%	(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
✓	97.6%	(.f64 #s(approx (/ (/ 4/3 (PI)) ( (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (fma.f64 v v #s(literal 1 binary64)))
✓	97.6%	#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Compiler

Compiled 259 to 123 computations (52.5% saved)

regimes13.0ms (0.2%)

Memory

30.5MiB live, 30.5MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(approx (/ (/ 4/3 (PI)) ( (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (fma.f64 v v #s(literal 1 binary64)))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
(.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))) (fma.f64 v v #s(literal 1 binary64)))

Outputs

(*.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))) (fma.f64 v v #s(literal 1 binary64)))

Calls

4 calls:

4.0ms	v
3.0ms	(*.f64 v v)
3.0ms	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
3.0ms	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Results

Accuracy	Segments	Branch
100.0%	1	`v`
100.0%	1	`(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))`
100.0%	1	`(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))`
100.0%	1	`(*.f64 v v)`

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes15.0ms (0.2%)

Memory

-7.5MiB live, 30.7MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(approx (/ (/ 4/3 (PI)) ( (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (fma.f64 v v #s(literal 1 binary64)))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) (fma.f64 (.f64 v v) #s(literal -3 binary64) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Outputs
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))

Calls

4 calls:

5.0ms	(*.f64 v v)
3.0ms	v
3.0ms	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
3.0ms	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Results

Accuracy	Segments	Branch
99.1%	1	`v`
99.1%	1	`(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))`
99.1%	1	`(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))`
99.1%	1	`(*.f64 v v)`

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes10.0ms (0.1%)

Memory

-15.7MiB live, 21.9MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(approx (/ (/ 4/3 (PI)) ( (sqrt (+ (* v (* v -6)) 2)) (- 1 (* v (* v (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (fma.f64 v v #s(literal 1 binary64)))
(/.f64 #s(literal 4 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(approx (* (* 3 (PI)) (- 1 (* v v))) (*.f64 (PI.f64) #s(literal 3 binary64)))))
(/.f64 #s(literal 4 binary64) (.f64 #s(approx ( (* 3 (PI)) (- 1 (* v v))) (.f64 (PI.f64) #s(literal 3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (*.f64 v v))))))

Outputs
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))

Calls

4 calls:

4.0ms	v
2.0ms	(*.f64 v v)
2.0ms	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))
2.0ms	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))

Results

Accuracy	Segments	Branch
99.1%	1	`v`
99.1%	1	`(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))`
99.1%	1	`(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))`
99.1%	1	`(*.f64 v v)`

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes5.0ms (0.1%)

Memory

15.2MiB live, 15.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Outputs
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Calls

4 calls:

1.0ms	v
1.0ms	(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))
1.0ms	(*.f64 v v)
1.0ms	(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))

Results

Accuracy	Segments	Branch
97.6%	1	`v`
97.6%	1	`(/.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v))))))`
97.6%	1	`(.f64 (.f64 (.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 6 binary64) (.f64 v v)))))`
97.6%	1	`(*.f64 v v)`

Compiler

Compiled 46 to 33 computations (28.3% saved)

simplify8.0ms (0.1%)

Memory

15.5MiB live, 15.5MiB allocated

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
10×	`distribute-lft-neg-in_binary64`
10×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	92
1	67	92
2	78	92
3	89	92
4	97	92
5	100	92
6	101	92

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))) (fma.f64 v v #s(literal 1 binary64)))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

Outputs
(.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (.f64 v v)))))) (fma.f64 v v #s(literal 1 binary64)))
(/.f64 #s(literal 4/3 binary64) (.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(/.f64 #s(literal 4/3 binary64) #s(approx (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))

soundness464.0ms (5.3%)

Memory

-13.6MiB live, 377.7MiB allocated

Rules

15 354×	`lower-fma.f64`
15 354×	`lower-fma.f32`
10 068×	`lower-fma.f64`
10 068×	`lower-fma.f32`
6 414×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	382	6348
1	1234	5398
2	5051	5163
0	8358	4975
0	241	1610
1	747	1426
2	2954	1351
0	8247	1301
0	16	67
0	26	67
1	101	65
2	626	65
3	5771	65
0	8439	58

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 92 to 58 computations (37% saved)

preprocess35.0ms (0.4%)

Memory: -7.9MiB live, 108.0MiB allocated
Remove: (abs v)
Compiler: Compiled 210 to 124 computations (41% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze4.0ms (0%)

sample1.1s (12.2%)

preprocess324.0ms (3.7%)

explain217.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify362.0ms (4.2%)

localize73.0ms (0.8%)

series10.0ms (0.1%)

simplify730.0ms (8.4%)

rewrite927.0ms (10.7%)

eval76.0ms (0.9%)

prune96.0ms (1.1%)

simplify326.0ms (3.8%)

localize163.0ms (1.9%)

series16.0ms (0.2%)

simplify713.0ms (8.2%)

rewrite535.0ms (6.2%)

eval273.0ms (3.1%)

prune260.0ms (3%)

simplify274.0ms (3.2%)

localize191.0ms (2.2%)

series15.0ms (0.2%)

simplify543.0ms (6.3%)

rewrite576.0ms (6.6%)

eval169.0ms (1.9%)

prune200.0ms (2.3%)

regimes13.0ms (0.2%)

regimes15.0ms (0.2%)

regimes10.0ms (0.1%)

regimes5.0ms (0.1%)

simplify8.0ms (0.1%)

soundness464.0ms (5.3%)

preprocess35.0ms (0.4%)

end0.0ms (0%)

Profiling